The Senkaku Islands, also known as the Diaoyu Islands, are claimed by both the PRC and ROC as an island chain under the Yilan County of Taiwan.
The historical context for this island claim is the most absurd: neither the PRC nor ROC were invited to the San Francisco Peace Treaty talks with Japan. A few months prior, the ROC’s Chiang Kai-Shek had signed the Potsdam Declaration with Allied leaders and explicitly declared which islands Japan could hold sovereignty over (the Senkakus were, notably, excluded). However, de facto sovereignty was overseen by the US until 1972, when the Okinawa Reversion shifted sovereignty to Japan.
If there is one territorial claim where the PRC and ROC are in the right with, it’s this one… Not the random claims the ROC has with Mongolia, Pakistan, Russia, Bhutan, Myanmar, Afghanistan, or Tajikistan (for which the PRC has negotiated and settled with), but for this attempt by Allied powers to ostracize a weak China and discredit the sacrifice of Chinese lives post-WW2.